Over the last century or so (1900 or so), there have been 461 named ships in the USN named after fish; of which 327 names were unique.

The top names (sorted by number of reuses and then alphabetically) are:

Wahoo: 5 vessels
Grayling: 4 vessels
Seawolf: 4 vessels
Shark: 4 vessels
Barb: 3 vessels
Barracuda: 3 vessels
Bonita: 3 vessels
Grampus: 3 vessels
Narwhal: 3 vessels
Nautilus: 3 vessels
Pickerel: 3 vessels
Plunger: 3 vessels
Salmon: 3 vessels
Sculpin: 3 vessels
Silversides: 3 vessels
Skate: 3 vessels
Skipjack: 3 vessels
Sturgeon: 3 vessels
Tang: 3 vessels
Walrus: 3 vessels

The raw data for all 461 names is available (HERE) in a CSV file.

Below is a list of all 327 unique names for fish-names in the USN (Click HERE to download a TXT file with just these names).

Abadejo
Acedia
Acoupa
Adder
Albacore
Amberjack
Angler
Apogon
Archerfish
Argonaut
Arnillo
Aspro
Atule
Awa
Balao
Bang
Banta?
Barb
Barbel
Barbero
Barracuda
Bashaw
Bass
Batfish
Baya
Becdna
Bergall
Besugo
Billfish
Blackfin
Blackfish
Blanquillo
Blenny
Blower
Blueback
Bluefish
Bluegill
Boarfish
Bocaccio
Bonaci
Bonefish
Bonita
Bowfin
Bream
Brill
Bugara
Bullhead
Bumper
Burrfish
Cabezon
Cabrilla
Cachalot
Caiman
Capelin
Capidoli
Capitaine
Carbonero
Carp
Catfish
Cavalla
Cero
Charoca?
Charr
Chickwick
Chicolar
Chivo
Chopper
Chub
Cisco
Clamagore
Cobbler
Cobia
Cochino
Cod
Comber
Conger
Corporal
Corsair
Corvina
Crevalle
Croaker
Cubera
Cusk
Cutlass
Cuttlefish
Dace
Darter
Dentuda
Devilfish
Diablo
Diodon
Dogfish
Dolphin
Doncella
Dorado
Dory
Dragonet
Drum
Dugong
Eel
Entemedor
Escolar
Espada
Fanegal
Finback
Flasher
Flier
Flounder
Flying Fish
Friar
Gabilan
Gar
Garfish
Garlopa
Garrupa
Gato
Goldring
Golet
Grampus
Grayback
Grayling
Greenfish
Greenling
Grenadier
Grouper
Growler
Grunion
Guardfish
Guavina
Gudgeon
Guitarro
Gunnel
Gurnard
Hackleback
Haddo
Haddock
Hake
Halfbeak
Halibut
Hammerhead
Harder
Hardhead
Hawkbill
Herring
Hoe
Holland
Icefish
Irex
Jack
Jallao
Jawfish
Kete
Kingfish
Kraken
Lagarto
Lamprey
Lancetfish
Lapon
Ling
Lionfish
Lizardfish
Loggerhead
Lucifer?
Macabi
Mackerel
Makaira?
Manta
Mapiro
Marlin
Medregal
Menhaden
Mero
Mingo
Moccasin
Moray
Muskallunge
Narcine?
Narwhal
Nautilus
Needlefish
Nerka
Obispo
Octopus
Odax
Ojanca
Ono
Orca
Paddle
Pampanito
Parche
Pargo
Perch
Permit
Peto
Pickerel
Picuda
Pike
Pilotfish
Pinna
Pintado
Pipefish
Piper
Piranha
Plaice
Plunger
Pogy
Pollack
Pomfret
Pomodon
Pompano
Pompon
Porpoise
Pudiano
Puffer
Queenfish
Quillback
Rasher
Raton
Ray
Razorback
Redfin
Redfish
Remora
Requin
Robalo
Rock
Roncador
Ronquil
Runner
Sabalo
Sablefish
Sailfish
Salmon
Sand Lance
Sarda
Sargo
Saury
Sawfish
Scabbardfish
Scamp
Scorpion
Sculpin
Sea Cat
Sea Devil
Sea Dog
Sea Fox
Sea Leopard
Sea Owl
Sea Panther
Sea Poacher
Sea Robin
Seadragon
Seahorse
Seal
Sealion
Searaven
Seawolf
Segundo
Sennet
Senorita
Shad
Shark
Shiner
Silversides
Sirago
Skate
Skipjack
Snapper
Snook
Sole
Spadefish
Spearfish
Spikefish
Spinax
Spot
Springer
Squalus
Steelhead
Sterlet
Stickleback
Stingray
Sturgeon
Sunfish
Swordfish
Tambor
Tang
Tarantula
Tarpon
Tautog
Tench
Texgon?
Thornback
Thrasher
Threadfin
Thresher
Tiburon
Tigrone
Tilefish
Tinosa
Tirante
Tiru
Tomtate
Toro
Torsk
Trembler
Trepang
Trigger
Triton
Trout
Trumpetfish
Trutta
Tullibee
Tuna
Tunny
Turbot
Tusk
Ulua
Unicorn
Vendace
Viper
Volador
Wahoo
Walrus
Whale
Whitefish
Whiting
Wolffish